Death in Paradise, BBC One

You'd think a lengthy shoot on the Caribbean island of Guadeloupe would be any actor's dream, but apparently Ben Miller found making Death in Paradise too hot and uncomfortable. That means he's perfectly cast as DI Richard Poole, a detective from the Metropolitan Police sent (as the drama would have it) to Saint-Marie, a fictional small island near Guadeloupe, to investigate the murder of a fellow British cop, Charlie Hulme.

Poole can't stand the Caribbean either, because the light's too bright, the sand is too sandy, and he feels the heat especially acutely because his luggage hasn't arrived and he's stuck with the suit he arrived in. Anybody else would at least remove their jacket and tie, but Poole is a bit of an oddball, a man seemingly with little in the way of a social life and no interests beyond investigating crimes. He yearns nostalgically for Croydon, dreams fondly of "finally being cold again" and longs for drizzle. He phones home to ask his neighbour about his dustbins (DI Poole on faraway beach, pictured below).

The locals have never seen anything like him. The dead man, DI Hulme, had been the local police chief and had embraced the climate with shorts and tropical shirts. Saint-Marie is slow and sleepy and lacking in technical facilities, so any kind of forensic work has to be done by sending the evidence to the lab on Guadeloupe. However, as he tours the crime scene and amasses clues, Poole marches about like a man who's late for a COBRA meeting with the prime minister, barking out instructions to the bewildered local cops. He's oblivious to the Caribbean's elastic timekeeping and slow-motion lifestyle.

With seven more episodes to go, it's going to be interesting to see how they keep coming up with enough local deaths to justify Poole's continued presence on Saint-Marie, though I suppose that never stopped Midsomer Murders. Wheeling out a parade of guest stars is going to be one method of keeping the jalopy puttering along, and this opener featured Rupert Graves as James Lavender, a wealthy and smarmy expat seemingly involved in a people-smuggling racket, as well as Lenora Crichlow as local policewoman Lily Thomson.

The story (by first-time screenwriter Robert Thorogood) flung a thicket of red herrings in Poole's path. Since Hulme's body was found alone inside a locked panic room which couldn't be opened from the inside, how had the killer managed to escape? How come party-goers in the garden had heard a gunshot, yet the .22 weapon that killed Hulme wasn't loud enough to have been heard outside the house? Why was the victim's cold, dead hand clenched around an antique travel guide? And why did Hulme have a stash of fake passports and bundles of dollar bills?

But the plotting and detection is only one aspect of Death in Paradise. Rather like a tropical Bergerac, the notion is evidently to bring a little taste of the exotic into our living rooms as the autumn evenings turn colder. The local coppers, Dwayne and Fidel (Danny John-Jules and Gary Carr), do a gentle comic double act, while Commissioner Patterson (Don Warrington) lends avuncular bulk and a sonorous baritone voice.

On top of that, since this is a co-production with France Télévisions, there had to be a French co-star, who arrived in the lissome shape of Sara Martins ("They form a beautiful French-British couple, and will share great adventures together," according to the French company). Inevitably their relationship got off on the wrong foot, with Poole arresting Martins' Camille Bordey for her suspicious behaviour aboard Lavender's boat, only to find that she was a French undercover cop (Poole and Camille Bordey, pictured above).

Much will doubtless be made of the comic contrast between svelte, sexy Camille and uptight, nerdy DI Poole, but the latter (played with bumbling wryness by Miller) has a few tricks up his sleeve. Despite appearances, he seems to be an uncannily brilliant detective, since the episode concluded with his unexpected Poirot-style unravelling of the Hulme murder case. Never mind that most of his revelations required imaginative leaps verging on the telepathic. It's all very charming and rather quaint, but is it built for the long haul?